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Simplifying -8x2 + 14x = 12 Reorder the terms: 14x + -8x2 = 12 Solving 14x + -8x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 14x + -8x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 14x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 7x + -4x2)' equal to zero and attempt to solve: Simplifying -6 + 7x + -4x2 = 0 Solving -6 + 7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.5 + -1.75x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.75x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.75x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.75x + x2 = 0 + -1.5 -1.75x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -1.75x + x2 = -1.5 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -1.5 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -1.5 + 0.765625 Combine like terms: -1.5 + 0.765625 = -0.734375 0.765625 + -1.75x + x2 = -0.734375 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = -0.734375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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